Note

You can download this example as a Jupyter notebook or start it in interactive mode.

Simple electricity market examples#

This example gradually builds up more and more complicated energy-only electricity markets in PyPSA, starting from a single bidding zone, going up to multiple bidding zones connected with transmission (NTCs) along with variable renewables and storage.

Preliminaries#

Here libraries are imported and data is defined.

[1]:

import numpy as np

import pypsa

[2]:

# marginal costs in EUR/MWh
marginal_costs = {"Wind": 0, "Hydro": 0, "Coal": 30, "Gas": 60, "Oil": 80}

# power plant capacities (nominal powers in MW) in each country (not necessarily realistic)
power_plant_p_nom = {
    "South Africa": {"Coal": 35000, "Wind": 3000, "Gas": 8000, "Oil": 2000},
    "Mozambique": {
        "Hydro": 1200,
    },
    "Swaziland": {
        "Hydro": 600,
    },
}

# transmission capacities in MW (not necessarily realistic)
transmission = {
    "South Africa": {"Mozambique": 500, "Swaziland": 250},
    "Mozambique": {"Swaziland": 100},
}

# country electrical loads in MW (not necessarily realistic)
loads = {"South Africa": 42000, "Mozambique": 650, "Swaziland": 250}

Single bidding zone with fixed load, one period#

In this example we consider a single market bidding zone, South Africa.

The inelastic load has essentially infinite marginal utility (or higher than the marginal cost of any generator).

[3]:

country = "South Africa"

network = pypsa.Network()

network.add("Bus", country)

for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        f"{country} {tech}",
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
    )


network.add("Load", f"{country} load", bus=country, p_set=loads[country])

[3]:

Index(['South Africa load'], dtype='object')

[4]:

# Run optimisation to determine market dispatch
network.optimize()

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['South Africa'], dtype='object', name='Bus')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 4 primals, 9 duals
Objective: 1.29e+06
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.

Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP   linopy-problem-_st3s7po has 9 rows; 4 cols; 12 nonzeros
Coefficient ranges:
  Matrix [1e+00, 1e+00]
  Cost   [3e+01, 8e+01]
  Bound  [0e+00, 0e+00]
  RHS    [2e+03, 4e+04]
Presolving model
1 rows, 3 cols, 3 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve : Reductions: rows 0(-9); columns 0(-4); elements 0(-12) - Reduced to empty
Solving the original LP from the solution after postsolve
Model name          : linopy-problem-_st3s7po
Model status        : Optimal
Objective value     :  1.2900000000e+06
Relative P-D gap    :  0.0000000000e+00
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-2ygbn8c_.sol

[4]:

('ok', 'optimal')

[5]:

# print the load active power (P) consumption
network.loads_t.p

[5]:

Load	South Africa load
snapshot
now	42000.0

[6]:

# print the generator active power (P) dispatch
network.generators_t.p

[6]:

Generator	South Africa Coal	South Africa Wind	South Africa Gas	South Africa Oil
snapshot
now	35000.0	3000.0	4000.0	-0.0

[7]:

# print the clearing price (corresponding to gas)
network.buses_t.marginal_price

[7]:

Bus	South Africa
snapshot
now	60.0

Two bidding zones connected by transmission, one period#

In this example we have bidirectional transmission capacity between two bidding zones. The power transfer is treated as controllable (like an A/NTC (Available/Net Transfer Capacity) or HVDC line). Note that in the physical grid, power flows passively according to the network impedances.

[8]:

network = pypsa.Network()

countries = ["Mozambique", "South Africa"]

for country in countries:
    network.add("Bus", country)

    for tech in power_plant_p_nom[country]:
        network.add(
            "Generator",
            f"{country} {tech}",
            bus=country,
            p_nom=power_plant_p_nom[country][tech],
            marginal_cost=marginal_costs[tech],
        )

    network.add("Load", f"{country} load", bus=country, p_set=loads[country])

    # add transmission as controllable Link
    if country not in transmission:
        continue

    for other_country in countries:
        if other_country not in transmission[country]:
            continue

        # NB: Link is by default unidirectional, so have to set p_min_pu = -1
        # to allow bidirectional (i.e. also negative) flow
        network.add(
            "Link",
            f"{country} - {other_country} link",
            bus0=country,
            bus1=other_country,
            p_nom=transmission[country][other_country],
            p_min_pu=-1,
        )

[9]:

network.optimize()

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['Mozambique', 'South Africa'], dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['South Africa - Mozambique link'], dtype='object', name='Link')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 6 primals, 14 duals
Objective: 1.26e+06
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Link-fix-p-lower, Link-fix-p-upper were not assigned to the network.

Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP   linopy-problem-s95dznly has 14 rows; 6 cols; 19 nonzeros
Coefficient ranges:
  Matrix [1e+00, 1e+00]
  Cost   [3e+01, 8e+01]
  Bound  [0e+00, 0e+00]
  RHS    [5e+02, 4e+04]
Presolving model
1 rows, 3 cols, 3 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve : Reductions: rows 0(-14); columns 0(-6); elements 0(-19) - Reduced to empty
Solving the original LP from the solution after postsolve
Model name          : linopy-problem-s95dznly
Model status        : Optimal
Objective value     :  1.2600000000e+06
Relative P-D gap    :  0.0000000000e+00
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-xvbjm56p.sol

[9]:

('ok', 'optimal')

[10]:

network.loads_t.p

[10]:

Load	Mozambique load	South Africa load
snapshot
now	650.0	42000.0

[11]:

network.generators_t.p

[11]:

Generator	Mozambique Hydro	South Africa Coal	South Africa Wind	South Africa Gas	South Africa Oil
snapshot
now	1150.0	35000.0	3000.0	3500.0	-0.0

[12]:

network.links_t.p0

[12]:

Link	South Africa - Mozambique link
snapshot
now	-500.0

[13]:

# print the clearing price (corresponding to water in Mozambique and gas in SA)
network.buses_t.marginal_price

[13]:

Bus	Mozambique	South Africa
snapshot
now	-0.0	60.0

[14]:

# link shadow prices
network.links_t.mu_lower

[14]:

Link
snapshot
now

Three bidding zones connected by transmission, one period#

In this example we have bidirectional transmission capacity between three bidding zones. The power transfer is treated as controllable (like an A/NTC (Available/Net Transfer Capacity) or HVDC line). Note that in the physical grid, power flows passively according to the network impedances.

[15]:

network = pypsa.Network()

countries = ["Swaziland", "Mozambique", "South Africa"]

for country in countries:
    network.add("Bus", country)

    for tech in power_plant_p_nom[country]:
        network.add(
            "Generator",
            f"{country} {tech}",
            bus=country,
            p_nom=power_plant_p_nom[country][tech],
            marginal_cost=marginal_costs[tech],
        )

    network.add("Load", f"{country} load", bus=country, p_set=loads[country])

    # add transmission as controllable Link
    if country not in transmission:
        continue

    for other_country in countries:
        if other_country not in transmission[country]:
            continue

        # NB: Link is by default unidirectional, so have to set p_min_pu = -1
        # to allow bidirectional (i.e. also negative) flow
        network.add(
            "Link",
            f"{country} - {other_country} link",
            bus0=country,
            bus1=other_country,
            p_nom=transmission[country][other_country],
            p_min_pu=-1,
        )

[16]:

network.optimize()

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['Swaziland', 'Mozambique', 'South Africa'], dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['Mozambique - Swaziland link', 'South Africa - Swaziland link',
       'South Africa - Mozambique link'],
      dtype='object', name='Link')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 9 primals, 21 duals
Objective: 1.24e+06
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Link-fix-p-lower, Link-fix-p-upper were not assigned to the network.

Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP   linopy-problem-syk2n9u0 has 21 rows; 9 cols; 30 nonzeros
Coefficient ranges:
  Matrix [1e+00, 1e+00]
  Cost   [3e+01, 8e+01]
  Bound  [0e+00, 0e+00]
  RHS    [1e+02, 4e+04]
Presolving model
2 rows, 5 cols, 6 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve : Reductions: rows 0(-21); columns 0(-9); elements 0(-30) - Reduced to empty
Solving the original LP from the solution after postsolve
Model name          : linopy-problem-syk2n9u0
Model status        : Optimal
Objective value     :  1.2450000000e+06
Relative P-D gap    :  0.0000000000e+00
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-yco8cou7.sol

[16]:

('ok', 'optimal')

[17]:

network.loads_t.p

[17]:

Load	Swaziland load	Mozambique load	South Africa load
snapshot
now	250.0	650.0	42000.0

[18]:

network.generators_t.p

[18]:

Generator	Swaziland Hydro	Mozambique Hydro	South Africa Coal	South Africa Wind	South Africa Gas	South Africa Oil
snapshot
now	600.0	1050.0	35000.0	3000.0	3250.0	-0.0

[19]:

network.links_t.p0

[19]:

Link	Mozambique - Swaziland link	South Africa - Swaziland link	South Africa - Mozambique link
snapshot
now	-100.0	-250.0	-500.0

[20]:

# print the clearing price (corresponding to hydro in S and M, and gas in SA)
network.buses_t.marginal_price

[20]:

Bus	Swaziland	Mozambique	South Africa
snapshot
now	-0.0	-0.0	60.0

[21]:

# link shadow prices
network.links_t.mu_lower

[21]:

Link
snapshot
now

Single bidding zone with price-sensitive industrial load, one period#

In this example we consider a single market bidding zone, South Africa.

Now there is a large industrial load with a marginal utility which is low enough to interact with the generation marginal cost.

[22]:

country = "South Africa"

network = pypsa.Network()

network.add("Bus", country)

for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        f"{country} {tech}",
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
    )

# standard high marginal utility consumers
network.add("Load", f"{country} load", bus=country, p_set=loads[country])

# add an industrial load as a dummy negative-dispatch generator with marginal utility of 70 EUR/MWh for 8000 MW
network.add(
    "Generator",
    f"{country} industrial load",
    bus=country,
    p_max_pu=0,
    p_min_pu=-1,
    p_nom=8000,
    marginal_cost=70,
)

[22]:

Index(['South Africa industrial load'], dtype='object')

[23]:

network.optimize()

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['South Africa'], dtype='object', name='Bus')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 5 primals, 11 duals
Objective: 1.25e+06
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.

Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP   linopy-problem-z039pblg has 11 rows; 5 cols; 15 nonzeros
Coefficient ranges:
  Matrix [1e+00, 1e+00]
  Cost   [3e+01, 8e+01]
  Bound  [0e+00, 0e+00]
  RHS    [2e+03, 4e+04]
Presolving model
1 rows, 4 cols, 4 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve : Reductions: rows 0(-11); columns 0(-5); elements 0(-15) - Reduced to empty
Solving the original LP from the solution after postsolve
Model name          : linopy-problem-z039pblg
Model status        : Optimal
Objective value     :  1.2500000000e+06
Relative P-D gap    :  0.0000000000e+00
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-q7q56m1m.sol

[23]:

('ok', 'optimal')

[24]:

network.loads_t.p

[24]:

Load	South Africa load
snapshot
now	42000.0

[25]:

# NB only half of industrial load is served, because this maxes out
# Gas. Oil is too expensive with a marginal cost of 80 EUR/MWh
network.generators_t.p

[25]:

Generator	South Africa Coal	South Africa Wind	South Africa Gas	South Africa Oil	South Africa industrial load
snapshot
now	35000.0	3000.0	8000.0	-0.0	-4000.0

[26]:

network.buses_t.marginal_price

[26]:

Bus	South Africa
snapshot
now	70.0

Single bidding zone with fixed load, several periods#

In this example we consider a single market bidding zone, South Africa.

We consider multiple time periods (labelled [0,1,2,3]) to represent variable wind generation.

[27]:

country = "South Africa"

network = pypsa.Network()

# snapshots labelled by [0,1,2,3]
network.set_snapshots(range(4))

network.add("Bus", country)

# p_max_pu is variable for wind
for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        f"{country} {tech}",
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
        p_max_pu=([0.3, 0.6, 0.4, 0.5] if tech == "Wind" else 1),
    )

# load which varies over the snapshots
network.add(
    "Load",
    f"{country} load",
    bus=country,
    p_set=loads[country] + np.array([0, 1000, 3000, 4000]),
)

[27]:

Index(['South Africa load'], dtype='object')

[28]:

network.optimize()

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['South Africa'], dtype='object', name='Bus')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 16 primals, 36 duals
Objective: 6.08e+06
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.

Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP   linopy-problem-urh2cpvw has 36 rows; 16 cols; 48 nonzeros
Coefficient ranges:
  Matrix [1e+00, 1e+00]
  Cost   [3e+01, 8e+01]
  Bound  [0e+00, 0e+00]
  RHS    [9e+02, 5e+04]
Presolving model
4 rows, 12 cols, 12 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve : Reductions: rows 0(-36); columns 0(-16); elements 0(-48) - Reduced to empty
Solving the original LP from the solution after postsolve
Model name          : linopy-problem-urh2cpvw
Model status        : Optimal
Objective value     :  6.0820000000e+06
Relative P-D gap    :  0.0000000000e+00
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-40asc9h_.sol

[28]:

('ok', 'optimal')

[29]:

network.loads_t.p

[29]:

Load	South Africa load
snapshot
0	42000.0
1	43000.0
2	45000.0
3	46000.0

[30]:

network.generators_t.p

[30]:

Generator	South Africa Coal	South Africa Wind	South Africa Gas	South Africa Oil
snapshot
0	35000.0	900.0	6100.0	-0.0
1	35000.0	1800.0	6200.0	-0.0
2	35000.0	1200.0	8000.0	800.0
3	35000.0	1500.0	8000.0	1500.0

[31]:

network.buses_t.marginal_price

[31]:

Bus	South Africa
snapshot
0	60.0
1	60.0
2	80.0
3	80.0

Single bidding zone with fixed load and storage, several periods#

In this example we consider a single market bidding zone, South Africa.

We consider multiple time periods (labelled [0,1,2,3]) to represent variable wind generation. Storage is allowed to do price arbitrage to reduce oil consumption.

[32]:

country = "South Africa"

network = pypsa.Network()

# snapshots labelled by [0,1,2,3]
network.set_snapshots(range(4))

network.add("Bus", country)

# p_max_pu is variable for wind
for tech in power_plant_p_nom[country]:
    network.add(
        "Generator",
        f"{country} {tech}",
        bus=country,
        p_nom=power_plant_p_nom[country][tech],
        marginal_cost=marginal_costs[tech],
        p_max_pu=([0.3, 0.6, 0.4, 0.5] if tech == "Wind" else 1),
    )

# load which varies over the snapshots
network.add(
    "Load",
    f"{country} load",
    bus=country,
    p_set=loads[country] + np.array([0, 1000, 3000, 4000]),
)

# storage unit to do price arbitrage
network.add(
    "StorageUnit",
    f"{country} pumped hydro",
    bus=country,
    p_nom=1000,
    max_hours=6,  # energy storage in terms of hours at full power
)

[32]:

Index(['South Africa pumped hydro'], dtype='object')

[33]:

network.optimize()

WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['South Africa'], dtype='object', name='Bus')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.03s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 28 primals, 64 duals
Objective: 6.05e+06
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, StorageUnit-fix-p_dispatch-lower, StorageUnit-fix-p_dispatch-upper, StorageUnit-fix-p_store-lower, StorageUnit-fix-p_store-upper, StorageUnit-fix-state_of_charge-lower, StorageUnit-fix-state_of_charge-upper, StorageUnit-energy_balance were not assigned to the network.

Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP   linopy-problem-_vmleqxl has 64 rows; 28 cols; 95 nonzeros
Coefficient ranges:
  Matrix [1e+00, 1e+00]
  Cost   [3e+01, 8e+01]
  Bound  [0e+00, 0e+00]
  RHS    [9e+02, 5e+04]
Presolving model
8 rows, 24 cols, 35 nonzeros  0s
3 rows, 7 cols, 9 nonzeros  0s
Dependent equations search running on 3 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
3 rows, 7 cols, 9 nonzeros  0s
Presolve : Reductions: rows 3(-61); columns 7(-21); elements 9(-86)
Solving the presolved LP
Using EKK dual simplex solver - serial
  Iteration        Objective     Infeasibilities num(sum)
          0     0.0000000000e+00 Ph1: 0(0) 0s
          4     6.0460000000e+06 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model name          : linopy-problem-_vmleqxl
Model status        : Optimal
Simplex   iterations: 4
Objective value     :  6.0460000000e+06
Relative P-D gap    :  0.0000000000e+00
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-5ae7n8om.sol

[33]:

('ok', 'optimal')

[34]:

network.loads_t.p

[34]:

Load	South Africa load
snapshot
0	42000.0
1	43000.0
2	45000.0
3	46000.0

[35]:

network.generators_t.p

[35]:

Generator	South Africa Coal	South Africa Wind	South Africa Gas	South Africa Oil
snapshot
0	35000.0	900.0	6900.0	-0.0
1	35000.0	1800.0	7200.0	-0.0
2	35000.0	1200.0	8000.0	-0.0
3	35000.0	1500.0	8000.0	500.0

[36]:

network.storage_units_t.p

[36]:

StorageUnit	South Africa pumped hydro
snapshot
0	-800.0
1	-1000.0
2	800.0
3	1000.0

[37]:

network.storage_units_t.state_of_charge

[37]:

StorageUnit	South Africa pumped hydro
snapshot
0	800.0
1	1800.0
2	1000.0
3	-0.0

[38]:

network.buses_t.marginal_price

[38]:

Bus	South Africa
snapshot
0	60.0
1	60.0
2	60.0
3	80.0

Simple electricity market examples

Contents

Simple electricity market examples#

Preliminaries#

Single bidding zone with fixed load, one period#

Two bidding zones connected by transmission, one period#

Three bidding zones connected by transmission, one period#

Single bidding zone with price-sensitive industrial load, one period#

Single bidding zone with fixed load, several periods#

Single bidding zone with fixed load and storage, several periods#